The manual is devoted to the methodology for preparing for olympiads in mathematics for students in grades 5-8. Among the various areas of training, the methodology for organizing and conducting a school mathematics circle is discussed in detail. Detailed developments of 17 circle classes are proposed, the basis of which is the solution of olympiad problems. The appendix provides options for municipal mathematics olympiads for students in grades 5-8. The book is addressed to both math teachers and students. It will also be useful for students of pedagogical universities.